MathsTEAM case studies resources

The Transition Module is designed to audit the mathematical skills of incoming students and thereby design and implement appropriate teaching, learning and assessment strategies to ease the transition to university.

Problem classes are traditionally used in the teaching of mathematics. For a first year Chemical Engineering course in mathematical modelling, a quiz based on the TV programme Ã¢??Who Wants to Be a Millionaire?Ã¢?? has been introduced, in a problem class supporting lectures. Following group work, with one set problem per group, students present their solutions to the rest of the class. The quiz follows the presentations. Each group is represented by a volunteer, who attempts to win chocolate prizes. The questions are both general, and specific to the particular problem done by the group. Besides reinforcing earlier learning, the quiz is fun. Certainly it appears to have been appreciated by two successive student cohorts. The lecturer and postgraduate demonstrator have also enjoyed the problem classes more than traditional formats.

The teaching of mathematics and statistics forms part of a first year module, Scientific Inquiry, which is taken by students on undergraduate science courses. The range of mathematical backgrounds amongst the students is accommodated through a Virtual Learning Environment (VLE), supporting student-centred learning. The Case Study describes the philosophy of the module and how this is reflected in its structure, delivery, available materials and use of self-assessment.

New support mechanisms have been introduced for Engineering students in their first year at Lancaster University to help maintain standards in all subject areas that are underpinned by Mathematics. Resources that have already been developed by Loughborough University are being used in a slightly modified form to help students to work through and overcome any weakness in Mathematics. Help sheets from Engineering Maths First Aid Kit are used to reinforce student learning. All material is used with the help of tutors to form a good foundation for further studies.

MATLAB is the chosen simulation environment that is used throughout the Department of Electronic and Electrical Engineering. MATLAB is used by the students at several levels. It is used in earlier years as an 'Engineering' calculator that is useful for scientific calculations and visualisation particularly for complex analysis. As the course develops MATLAB becomes invaluable for investigating the time-frequency characterisation of signals and systems. MATLAB also gives the students an environment that allows them to write programming code in a 'C' like format. Finally MATLAB facilitates greater contextual teaching and problem based learning, which has become increasingly important in current Electronic and Electrical Engineering.

The Mathematics Department at Keele University has pioneered the use of diagnostic testing linked to Computer-Based Learning (CBL) self study modules for students entering Principal Mathematics. In particular, the department has invested in the use of Mathwise modules to provide support materials. Recent advances in software have produced a new generation of courseware but there is considerable inertia in changing to such new material without some evidence that students will benefit. This case study considers this problem and considers how diagnostic testing can be used to decide when to update the courseware being used.

The Mathematics Support Centre at Coventry University (originally known as the BP Maths Centre) was established in 1991. The Centre aims to provide early identification of problems and on-going support for individual students. This is achieved through use of diagnostic testing, the provision of a wide range of resources and the availability of one-to-one assistance on drop-in basis. The CentreÃ??Ã?Â¢??s website was launched in September 2000 to:

extend the support provision to students who did not find it easy to visit the Centre (e.g. part-time students).

provide access to a range of resources at times when the Centre is closed.

deliver new support activities such as online practice tests and email questions.

A few years ago the department of mathematics at Edinburgh looked at the problem of interfacing between mathematics and engineering courses and came up with a system to enable greater student understanding. The implementation of this system and how it is helping students is reviewed in this case study.

A paper-based diagnostic test of mathematical skills, presented to Stage 1 undergraduates, revealed that entrants encounter difficulties with some of the basic mathematical concepts that are essential if students are to successfully complete a programme of study within the biosciences. Students reacted favourably towards a number of computer-based learning materials aimed at supporting development of their basic mathematical skills through self-directed learning. However, the availability of such resources made no significant difference to the studentsÃ¢?? overall performance in a subsequent test. Some issues and applications are discussed.

Students arriving in many of the UMIST departments are required to take a brief maths test on arrival. Mathematics students who underachieve on this test are assigned some questions relevant to sections where they did poorly and also referred to sections from texts and Internet notes. The studentÃ?Â¢??s attempt at the assigned questions acts as a basis for a feedback session. Certain students in other departments (receiving mathematics as a service course) are asked to complete a computerised assignment on areas where they underachieved. Again, they are provided with references to texts and Internet notes.

Students on Engineering awards at UWE come from a range of academic backgrounds that include A2/AS-Level, B-TEC, Foundation year, overseas qualifications and mature students who in some cases are returning to education after an absence of over ten years. Ensuring that individuals from such a diverse population can develop the necessary mathematical skills and knowledge to cope with the demands of an Engineering award is clearly difficult. In this case study we describe the development of diagnostic testing at UWE and its role in a strategy for teaching mathematics to a large mixed ability group.

A comprehensive collection of case studies,
intended to assist you with the challenge of enhancing the basic
mathematical skills of engineering or science students. These case studies
focus particularly on diagnostic testing.

Brunel is well advanced in promoting good practice in the use of Computer Aided Assessment (CAA). The diagnostic tests are of CAA type, delivered on-screen with full animation at the testing level required (post-GCSE or post A-Level). 200 students are involved on programmes ranging from financial computing to mathematics.

All students are assessed using a paper-based, but optically marked, written test of 12 multi-choice questions (MCQs). The test covers algebraic simplification, approximation, logs, trigonometry and calculus. It is based on a test developed at Coventry University. It is used to assess students' strengths upon entry.

Diagnostic testing at Coventry University encompasses various disciplines. Co-ordinated by the Maths Support Centre, the test is used to assess the students' ability and target appropriate mathematics support as early as possible. This case study reviews the testing process and how it is linked to appropriate support material, advice and learning resources.

All students are assessed via 20 computer-based multi-choice questions (MCQs). These questions are selected at random from a large question bank, developed jointly by Nottingham and Keele Universities. The main objective is to provide a profile of each studentâ??s mathematical abilities. Each question tests a number of different skills simultaneously and hence contributes to an assessment of the different aspects of this profile. The profile becomes a diagnostic report, which then directs each student to a series of specific modules in â??Mathwiseâ?? that will reinforce their knowledge and correct any problems.

Two weeks are spent doing revision prior to three diagnostic tests. These are designed to assess studentsÃ¢?? strengths and weaknesses after they have spent some time working in a mathematical context. The tests are all paper-based multi-choice questions (MCQs). They are hand-marked, but owing to the small number of students there is little time delay between assessment and distribution of the results.

All students are assessed using a paper-based written test of multi-choice questions (MCQs). The test has 15 questions of which the students must pass with 12 correct. Two hours were allowed. All of the questions were on routine arithmetic and algebra with emphasis on manipulative drill and practice, e.g. decomposition into powers of primes, long division, fractions, BODMAS, surds, elementary function definition, and inequalities. The test is quite demanding and was introduced last year 2001. It is repeated for those who fail six times during the course of the year in a programme called Ã¢??Essential MathematicsÃ¢??. Passing it is a mandatory requirement to proceed into the second year.

All students are assessed using a paper-based written test on their first day in the department. The students are allowed to use any non-graphical calculator to help answer 48 questions of the type and standard that they should be familiar with from A-Level. The questions range across simple arithmetic and algebra through logs to differentiation and integration, finishing with some questions on vectors. Final solutions are filled in on an answer grid. The temporary streaming of the students is based on the results.

All students are tested via two computer-based tests each consisting of 10 multi-choice questions (MCQs). These tests are set from a large bank of questions using the Ã¢??TALÃ¢?? (Teach And Learn) computer system developed at the University of Bristol. The topics covered include arithmetic, algebra, geometry, functions, calculus, and probability. A Ã¢??leave unansweredÃ¢?? option is provided and negative marking used to discourage guessing. The tests are accessed through a Web interface, so in principle could be accessed from anywhere. It has been run with large-scale simultaneous access and, although a little slow, is relatively robust.

School of Mechanical and Systems Engineering DIAGNOSYS has been used by the Department of Engineering Mathematics, now the School of Mechanical and Systems Engineering, since 1993. By 1996 there were five departments involved in using the software. Based on an interview with the administering lecturer and a student questionnaire this case study examines the procedure, results and student responses to the diagnostic testing process.

First year students in mathematics have been tested at the University of Sussex over the past 25 years using a paper-based diagnostic test. The test has hardly changed during that time. The test and remedial measures are co-ordinated by a senior member of staff, but administered by two postgraduates.

Since 1977 a paper-based diagnostic test has been presented to first year mathematics students at the University of York. Based on an interview with the administering lecturer and a student questionnaire this case study examines the procedure, results and student responses to the diagnostic testing process.

Students in Aeronautical Engineering are taught MATLAB in the first year to provide them with programming skills and for use in later courses. In the second year MATLAB is used to enhance the teaching of linear algebra and to apply the mathematical techniques to engineering problems.

The first summer mathematics course ran during July and August of 1997, financed by South Bank University (SBU). In subsequent years the course became HEFCE funded. The Fast Track mathematics course was a specifically designed free summer course to help equip the students with those skills required to enter a degree of Higher National Diploma in science or technology. SBU established the six week daytime course, which helped students identify gaps in their knowledge and provided a tailor made mathematics learning programme. This course now runs every summer to equip new students with the mathematical skills required for a smooth transition into university.

The Summer School has operated on the same general principles since 1991. It helps prepare students for entry into programmes for which they have a conditional offer. It features tailored instruction, flexible attendance and delivery and continuous supportive feedback.

The subject of A-Level mathematics has attracted a great deal of political and academic controversy. Those who represent the academic community in Higher Education have argued for over a decade that the standards of A-Level mathematics have been declining and continue to do so. Elsewhere it has been argued that much of the decline perceived by those who teach in engineering and science departments is more likely to be attributed to the very substantial national decline in entry standards to engineering and science courses rather than any real change in A-Level standards. Using available statistics, a study of the electronics students at York set out to discover whether these questions could be answered and the results
were published in a detailed paper [1] of which the following is a summary.

Mathematical Methods is a revision course for third year materials scientists. Started in 1997, there is no formal examination. It consists of six lectures, an examples class and a questions sheet, and provides revision of past topics, with examples relating to third year materials courses and a background for the fourth year. This case study reviews the course and its role in providing the student with a mathematical foundation in the context of materials science.

The Mathematics Summer School was run for the first time in September 2001, lasting one week immediately prior to the start of term. Many students admitted to courses in the School of Science and Technology are perceived to have major weaknesses in the type of fundamental algebra that underpins much of their analytical work, both in mathematics units per se and in other units. This development represents one strand of additional support given to such students; the fledgling Mathematics Support Unit can give such support as the course progresses. This initiative is not funded in any direct way and depends on the availability of already heavily committed staff.

During the early 1990s, mathematics software was written using Visual Basic for students at Bournemouth University. With the advent of the Java programming language, this software was translated and extended into MathinSite, a website containing mathematics applets (small programs that can be run through a web browser). The primary aim of these applets is to help deepen mathematical insight through dynamic, interactive visualisations. Use of the Internet not only ensures that the content can be delivered within a studentÃ?Â¢??s own educational surroundings, but also that any user can access the content any time of day or night from any computer in the world with an Internet connection.

A comprehensive collection of case studies,
intended to assist you with the challenge of enhancing the basic
mathematical skills of engineering or science students. These case studies
focus particularly on embedding mathematics within the disciplines of engineering and science.

A comprehensive collection of case studies,
intended to assist you with the challenge of enhancing the basic
mathematical skills of engineering or science students. These case studies
focus particularly on mathematics support.

The problem of declining mathematical skills and appetite amongst university entrants is well known. In order to soften the impact that this makes on student recruitment and retention in the School of Electronics at the University of Glamorgan, it became necessary to explore a 'minimal-math' or 'engineering-first' teaching approach. MATLAB-based graphical user interfaces, simulations and animations are employed to give students an unclouded insight into the engineering concept and the underlying physical considerations, and a clear appreciation of the interplay of the parameters involved. This type of first encounter helps to stimulate the students' interest in the subject, erects crucial knowledge pegs, and lays a solid foundation to support a more mathematically rigorous approach during later encounters with the topic when any deficiencies in math skills will have been remedied.

Mathematics is perceived as a difficult subject within engineering or science degree courses. Traditional lectures, with students passively listening to the lecturer or transcribing notes, do little for the studentsÃ¢?? image of mathematics. This style of lecturing and its lack of feedback can also be very unsatisfactory for the lecturer. In an attempt to overcome these problems, an element of interaction has been introduced into lectures. This has been achieved by encouraging communication via the Personal Response System, part of the Interactive Classroom developed by the Department of Mechanical Engineering, University of Strathclyde. Lectures are problem-based, with students immediately given the opportunity to put the methods they have learnt into practice.

The Open Learning Resource Centre (OLRC) at the School of Computing and Mathematics, University of Huddersfield provides a quiet environment with seated study places for up to sixty students. The Centre originally operated from 8.30am to 4.30pm every day but that has now been extended to cater for the needs of part-time students. Every day a tutor provides a surgery on a one-to-one basis to answer questions posed in mathematics, statistics or operational research (MSOR). It was also commended by the QAA Visiting Panel during a recent Teaching Quality Assessment.

Peer Support (PS) has been running in the Department of Mathematics and Computer Science at the University of Leicester for the past 9 years. In this scheme students from the second and third years (called leaders from now on) help first year students in their efforts to assimilate first year material. The help occurs in small timetabled groups containing up to 8 or 10 first years and 2 to 4 leaders. In its first year the scheme had 6 second year leaders and now we have typically between 15 and 20 second and third year leaders.The number of first year students taking part in the scheme has also grown from about 10% of students in the early years to around 50% of students making some use of the scheme at some stage in the year.

We describe a course aimed at providing chemical engineering students with an understanding of the fundamental classes of equations which occur in chemical engineering, the mathematical basis of their numerical solution methods and the basic methods of implementing these in a high level computing language. The course thus integrates elements of both conceptual and practical mathematics and computing.

EXCEL has been used to provide simulation facilities in support of teaching control to engineers. This dictates a sampled data approach which fits in naturally with digital implementation of control. The technique also allows students to explore the affects of non-linearities in systems such as control signal saturation. It provides a Ã¢??hands-onÃ¢?? dimension which students find valuable. The approach is capable of use with other dynamic systems and is not restricted to teaching control.

Many departments of mathematics, physics and engineering now use some form of diagnostic test to assess the basic mathematical skills of new undergraduates [1]. Results reveal that a typical cohort consists of students with a diverse range of mathematical backgrounds and capabilities. Tests also help to identify those students who lack both confidence and competence and are deemed to be at risk of failing or dropping out in Year One.
It is now commonplace for those teaching first year mathematics to be faced by an inhomogeneous student cohort and all are in accord that it has become almost impossible to teach them effectively together. It is against this background that streaming of first year undergraduate physicists into two more homogeneous groups has been introduced at the University of Leeds. The aim is to provide more effective teaching and mathematics support that will get students up to speed and mathematically prepared for their second year.

The date of the formal introduction of student proctors within the Faculty of Engineering and Information Sciences is unclear. However, we have certainly been using student proctors for more than ten years. The purpose is to offer students the opportunity to learn from their peers in a one-to-one situation. Within the Faculty three departments have a student proctor programme each of which runs in much the same way but with differences which reflect the different custom and practice of each department.

University College London has established a wide selection of teaching resources to support a dramatic increase in the number of entrants to the Mathematics Department. This includes a diagnostic test for all entrants, a workbook for students to complete before the first semester and an integrated system of tutorials, lectures and a problem class. An intense Bridging Course also provides students with a valuable and comprehensive perspective of university mathematics.

UMIST introduced a three level course structure to help students entering civil engineering, chemical engineering, electrical engineering, chemistry, mechanical engineering, computing and optometry to cope with the maths content of each of the courses. Based on previous qualifications and a diagnostic test, students are allocated places within the P, Q and R stream.

Mathematical Advice and Co-ordination Service (MACS) was established in 1995 within the Faculty of Mathematics to support students within their studies at the University and to help prepare them to go into the world. Funding was made available for an initial period of 3 years and was then continued on a year-to-year basis. The emphasis has changed over the years and most of the work is now linked to studentsÃ?Â¢?? current problems but also includes help for those facing employersÃ?Â¢?? tests at interview. The University accepted that the concept of student support offered in Mathematics needed to be extended into other areas and, through The Higher Education Funding Council for England (HEFCE), established the Student Advice Service (SAS). The SAS is now a permanent feature of the University serving any member of the student body (and indeed staff) who might benefit from what it offers. The remainder of this case study considers only the mathematical part of the SAS, though many of the comments apply to the other areas of the SAS (Academic English, Study Skills and ICT).

Nine years ago members of staff within Physical Sciences at Cambridge University began recognizing that some students were having problems not only with the Mathematics Courses but also with applying material from A level in the context of their scientific subjects. The mathematics workbook was introduced to assist students with revision prior to starting university.
On completion the student is asked to fill in a questionnaire that helps to define the problem areas. This is presented to their supervisor. The supervision system is a fundamental feature of Cambridge teaching and one of its main strengths. The student sees a supervisor Ã¢?? most commonly in a group of two undergraduates, sometimes in a group of three and only exceptionally one-on-one Ã¢?? to discuss his or her work for at least an hour once a week. Such support is ongoing and essentially provides individual attention to those students who lack fundamental mathematical skills.

The introduction of the graphics calculator has provided the fourth year students taking Science with Management Studies with an interactive learning tool. This case study reviews its introduction into the course Discrete and Continuous Models at Napier University.

The department of chemistry offers over two semesters, Mathematics for Chemists 1 and 2, which provide students with the understanding and use of mathematical techniques for various chemistry degrees. This case study reviews these courses and illustrates their value in terms of providing the students with a positive foundation for future study.

The approach to teaching Maths to Year 1 students in the Department of Engineering underwent a major reorganisation prior to the start of the 2002/3 session. The aim was to provide an optimum framework within which students studying four different engineering disciplines could be taught Maths within the resource constraints imposed by student numbers, and to cope with the extremely wide range of their Mathematical abilities on entry to these degree programmes. After much discussion, students are now taught their Year 1 Maths topics in two different cohorts, streamed according to initial Maths ability, and using different approaches in terms of the depth of understanding expected. This also involves the use of different assessments. This approach has been much more popular and created far fewer difficulties than the previous system which divided the students into two groups according to degree programme.

New entrants to chemistry degree programmes are given a 24 hour course in mathematics if they do not have an A level qualification in the subject. This concentrates only on the skills necessary to successfully complete the first year physical chemistry course; these include simple statistics, functions, partial differentiation and integration. The course is taught using chemically relevant examples, in an order related to the chemistry course rather than traditional mathematics courses.

Analysis is made showing how Helmholtz and Gibbs energies conveniently interrelate enabling typical 2-D and 3-D curves to be drawn across a range of temperature for selected chemical equilibria. Opposing influences leading to a free energy minimum or an entropy maximum are given a physical explanation with the attainment of equilibrium and the choice of conditions made evident. Simplifying assumptions are emphasised and the examples show how the data are manipulated, limits evaluated and trends in equilibrium summarised by EXCEL charts.

Mathematics is vital for civil engineers but its role is changing. Arup chairman Duncan Michael [1] has argued for less emphasis on the teaching of mathematics. Here we report on a necessary change of emphasis but also argue the importance of a good mathematical education for all engineers

The education Drop-in Centre at the University of Glamorgan was established during the academic year 1996/97. Its aim has always been to provide generic study support for students with writing and study skills as well as mathematics and statistics skills. Since its creation the Centre has been through a variety of changes in terms of staffing and layout. It has grown steadily each year and now comprises of two sites and seventeen staff, three full-time administrators and fourteen part-time tutors. The Centre is seen to play a key part in retaining students and has become part of the fabric of the University.

The Centre was established in 1996 within the Department of Mathematical Sciences in order to underpin the Department's service teaching commitment to engineering undergraduates. In the first instance funding had been made available through an internal university learning and teaching initiative for a period of two years. Because of its early successes the Centre became a permanent feature in 1998 and now serves any student in the university who might benefit from additional resources, over and above those normally provided, to help them in their learning of basic mathematical techniques.

Computer-based diagnostic testing has been used for new engineering students for some years at University of Newcastle upon Tyne. Follow-up support has been available only in some departments. In summer 2001, new students were issued (in advance or on arrival) with a Ã¢??Maths Revision BookletÃ¢?? covering the basic maths topics that we didnÃ¢??t intend to teach. Following the diagnostic test, lunchtime classes were offered for six weeks, based on the booklet, for those students who wished to attend.We report on the student opinion, analysis of diagnostic and examination performance.

The Maths Learning Centre (MLC) was first established as a library service in 1994 but initially struggled for funding and recognition at a wider University level. Since 2000 it has been incorporated into the centrally funded Student Learning Advisory Service (SLAS).

The Study Support Centre (SSC), within the Robert Gordon University (RGU), aims to provide students with assistance in Mathematics, Writing & Communication skills, Information & Communication Technology applications, Statistics, Study Skills and support for dyslexic students. The SSC offers students independent assistance through individual and small group tuition outwith their normal programme of study, as well as Computer Assisted Learning (CAL) packages, specialist software for special needs students and text based self-learning materials. The SSC has created a basic mathematics diagnostic assessment, which we give to first year students in many Schools. Currently, in collaboration with the School of Engineering, an engineering principles diagnostic assessment is being designed and implemented.

Wider access students i.e. those people who have narrowly missed the entrance requirements, are given a chance to "topup" their mathematical knowledge before entering Napier University. They can study at their own pace over the summer vacation. There is regular communication with a university tutor and extra study sessions are held during August at the University.

Mathcad is used in all years of the engineering mathematics course to enable students of civil engineering to investigate real engineering problems which have no analytical solution but which illustrate important mathematical concepts. In the second year engineering mathematics course Mathcad is used to assist in the teaching of numerical solutions of second order boundary value differential equations. Comparisons are made between classical analytical solutions and the numerical solutions.

Computer based assessment has been used at UWE for a number of years on certain modules run by the School of
Mathematical Sciences. In this case study we discuss the operation of the assessment for a first year engineering
mathematics module in which students are permitted multiple attempts and are allowed, within an specified period of time,
to choose when they take the assessment. Feedback from students has been highly positive about the assessment regime and our observation is that operating the tests in this way does encourage students to work steadily throughout the year.

Even as long ago as the mid-1990s, a survey for the Open Learning Foundation [1] found that most universities were using some form of mathematics diagnostic testing on their first-year undergraduates, usually during Induction Week. With the advent of computer-aided mathematics diagnostic systems such as DIAGNOSYS [2], it has become easier to obtain an off-the-shelf diagnostic system. Even so, many people still use their own in-house tests. This study considers one such example.

Quantum theory is a key part of the chemical and physical sciences. Traditionally, the teaching of quantum theory has relied heavily on the use of calculus to solve the SchrÃ?Â¶dinger equation for a limited number of special cases. This approach is not suitable for students who are weak in mathematics, for example, many students who are majoring in biochemistry, biological sciences, etc. This case study describes an approach based on approximate numerical solutions and graphical descriptions of the SchrÃ?Â¶dinger equation to develop a qualitative appreciation of quantum mechanics in an Australian University.

This case study reports on the approach at one institution to helping first year engineering students to acquire the
mathematical skills they need. The approach involves a range of support mechanisms, and the concerted use of technology
as well as paper and pencil methods. Changes in curriculum, pedagogy and indeed assessment style have all proven
necessary.

For first and second year engineering students at Napier University, the TI-83 graphics calculator plays a major role in an integrated technological approach to mathematics. This case study reviews the process of integration and its current position in the teaching of students.